It has been argued that the quality of mathematics education in the United States has deteriorated over a period of years. Students are not exhibiting depth of understanding of the subject and certainly are not developing an enthusiasm for it. Part of the reason for this lies in the abstract nature of mathematics itself, but part also lies in the way it is customarily taught. In many classrooms, the instructional sequence is as follows:
1. The teacher presents a technique or introduces a topic, usually by definition.
2. The students practice the technique or work on the topic.
3. A test is given to measure mastery of the technique or topic.
4. The teacher moves on to the next topic or technique.
Because of the inherent abstractness in mathematics, this pedagogical approach simply does not generate long-lasting success. Students often do not understand what they are learning and succeed more by mimicry than by genuine knowledge. Moreover, this approach tends to make students endure mathematics rather than enjoy it.